Do new competitors, new customers, new suppliers,... sustain, destroy or create competitive advantage?

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1 Do new competitors, new customers, new suppliers,... sustain, destroy or create competitive advantage? Glenn MacDonald Olin School o Business Washington University Michael Ryall Melbourne Business School University o Melbourne September 2006 Abstract A new player, e.g., an entrant, joining an existing game generally allows more value to be created, but also creates new alternatives or existing players. Greater value expands the range o equilibrium appropriation levels or an existing player, in particular, lowering the minimum equilibrium appropriation. The emergence o new alternatives has the opposite e ect. We say a player has competitive advantage i the player s minimum equilibrium appropriation is strictly greater than the player s outside alternative. That is, the orces o competition alone, as embodied in the conditions de ning equilibrium, su ce to guarantee a player appropriates more than the best alternative to being in the game, i.e., a sustainable perormance advantage. When a player has competitive advantage pre-entry, but not postentry, we say entry destroys competitive advantage; likewise or creating and sustaining competitive advantage. Our results provide complete characterizations (i.e., i and only i statements) o the eatures o a game that cause the addition o a new player to destroy, create or sustain competitive advantage in a general coalitional game. These results are o importance or strategy issues since as argued by proponents o value-based business strategy, e.g., Brandenburger and Stuart (1996) many o the economic interactions o interest in strategy are well-described as coalitional games. Comments rom seminars at Emory, Yale and HBS are greatly appreciated. 1

2 1 Introduction Many o the subjects o interest in strategy and industrial organization involve augmenting the agents in a game. Some examples: (i) a rm entering an industry with a new substitute or complementary product, or a new technology, or simply more capacity; (ii) a rm developing the capability to imitate an incumbent s activities, and contemplating entry; (iii) a new customer or segment changing demand or some product; (iv) an entrepreneurial venture altering the game incumbents are playing; (v) a spin-o or divestiture; (vi) a new source o supply or inputs; (vii) the transition rom pro table short run to zero pro t long run in a competitive market; (viii) a patent expiring and allowing others to produce; etc. This paper explores how increasing the number o agents in a game a ects the equilibrium payo s o existing agents. 1 Speci cally, we study a general coalitional game (within which any o the examples just mentioned can be described), and ask how adding an agent changes an existing agent s minimum equilibrium payo. We ocus primarily on whether that minimum payo is zero, or more generally, equal to the agent s next best alternative to being in the game. There is nothing about our methodology that requires this ocus on the minimum and whether it is zero; indeed, the same sort o reasoning can be applied to whether the minimum takes on some other value, or whether the maximum does so, etc. Instead, as we argued elsewhere (MacDonald and Ryall, 2004b), whether the minimum is positive is a question o special interest since it describes whether the orces o competition alone su ce to guarantee supra-normal pro t, an outcome we equate with the amiliar term competitive advantage. 2 1 Our results cover decreasing the number o agnets by, e.g., rm exit, simply by treating the game with the larger number o agents as the initial condition. 2 Competitive advantage is traditionally synonymous with pro table. In our view, this de nition obscures an important distinction in that it lumps competitive reasons or pro tability together with others such as luck, connections to regulators, negotiating skill, etc. Thus we restrict the term competitive advantage to a narrower meaning, viz. pro table as a consequence o competitive alternatives. 2

3 In our earlier work (MacDonald and Ryall (2004a) and (2204b)), we provided a complete characterization o an agent s having a competitive advantage in a general coalitional game, i.e., a rm s minimum equilibrium payo is positive i and only i certain conditions involving agents alternatives are satis ed. Loosely, the basic result rom that work (ormally restated below) was that there are precisely two opposing entities that shape how value must be distributed in equilibrium: (i) the value ultimately produced by the agents; and (ii) the value that could be generated via alternative activities available to agents. The value produced must ultimately be distributed among agents, and the more there is to distribute, the more ways there are to distribute it and still dominate agents alternative opportunities (i.e., alternatives the agents must be dissuaded rom pursuing i they are to participate in the contemplated value generating activities). Thus, more value to distribute widens the range o payo s an agent can earn in equilibrium, including lowering the minimum. On the other hand, agents alternatives constrain the ways in which the value produced can be distributed so as to dominate those alternatives. More/better alternatives make this e ect more powerul, thereby narrowing the range o equilibrium payo s or an agent, including increasing the minimum. 3 We ocus on comparing a rm s (generally, any agent s) pre- and post-entry competitive advantage. The result described above suggests that one way to proceed is to analyze the agent s appropriation in a pre-entry game, and then compare this to appropriation in the corresponding post-entry game, including the entrant o interest. This approach, which we adopt, allows us to develop propositions o the ollowing orm: a rm has competitive advantage pre-entry, but not post entry, i and only i condition X is satis ed in the pre-entry game, but not in the post-entry game; i.e., a complete description o the eatures o the pre-and post-entry games that lead to entry destroying competitive advantage. The eatures o the game that lead to the rm not having competitive advantage 3 In what ollows we will reer to the impact o agents alternatives as competition. That is, an agent s having alternatives means there are groups competing to engage the agent in other activities. 3

4 pre-entry, but having competitive advantage post-entry, are described in an analogous ashion; i.e., entry creates competitive advantage. Entry sustaining competitive advantage is de ned and characterized similarly. A simple, but important, insight that underlies our analysis is that the preand post-entry situations have much in common. That is, the two games are not simply a pair o games with di ering numbers o agents. Instead, adding an agent brings new value creation opportunities while leaving other others unchanged. By speciying the post-entry game ully, then, to analyze the pre-entry game, suppressing all value creation involving the entrant, we are able to provide a complete description o the eatures o the pre- and post-entry environments that result in entry destroying, creating, or sustaining competitive advantage; see Proposition 1. (The remaining case, in which the rm lacks competitive advantage pre- and post-entry, is described by none o the above conditions.) Loosely, an entrant generally brings additional value to the economic activities in which agents ultimately engage, tending to widen the range o possible equilibrium payo s or agents, including lowering their minimum payo s. But the entrant also creates new alternatives in which agents might engage, which has the opposite e ect. Whether entry creates, destroys or sustains competitive advantage depends on the interplay o these orces. Propositions 2-5 provide more perspective on entry s impact on competitive advantage by stating these conditions in terms o the entrant s added value. Entry s impact on an incumbent s minimum payo comes via exactly three avenues. First, pre-entry, the aggregate value that all agents could create without the entrant is exactly the value that can be distributed in the pre-entry game. Post-entry, obtaining this value becomes one o the alternatives that the set o all agents other than the entrant might act upon. Second, entry opens up a speci c alternative or the incumbent; i.e., to create value by interacting with just the entrant. Third, entry creates new opportunities or groups o agents that may or may not include the incumbent; i.e., to create value by interacting with the entrant. Alternatives o each variety have di erent e ects. Our second set o results, Propositions 6-8, extends our understanding o how entry impacts 4

5 competitive advantage by exploring the operation o these three e ects one at a time. Imitation is a speci c orm o entry, one much discussed in strategy. Indeed, i there is one idea that is not controversial, it is that to enjoy a sustained perormance advantage, a rm must possess value-producing resources that are di cult to imitate. For example, Saloner et. al. (2001, page 49) say, I a rm s competitive advantage is based on its capabilities, a sustainable advantage requires either that imitation is di cult or that the rm can improve its capabilities (learn) beore its rivals catch up. The intuition is as ollows. Imitation permits a competitor to provide new, equally attractive alternatives to customers. In order to persuade those customers not to act on those alternatives, the incumbent rm must allow its customers to keep a greater share o the gains rom trading with it than they had previously enjoyed. As a result, its payo is diminished and possibly eliminated altogether. In MacDonald and Ryall (2004b), we ormalized and explored two versions o this idea, and ound that the impact o imitation varies greatly with what one has in mind by ability to imitate. One version is what we called capability imitation: the imitator can do anything the incumbent can do, viz., a clone o the incumbent. More precisely, the entrant is a capability imitator i in every economic interaction involving the rm, replacing the rm with the imitator results in the same value created. We showed that (i) capability imitation might or might not eliminate competitive advantage, and (ii) entry orces both the rm and the entrant to earn the same range o payo s (not necessarily zero). Our second version o imitation, unlimited product imitation describes the situation in which the rm and its imitator can supply an identical product at the same constant marginal cost, i.e., no capacity constraints, no diminishing returns to scale, no limited managerial talent,... Unlimited product imitation invariably both eliminates competitive advantage and orces both the rm and entrant to earn zero payo. These are special cases o the more general phenomenon o entry studied in this paper. The use o coalitional game theory to study issues in strategy is growing 5

6 rapidly. The coalitional approach to strategy was rst suggested by Brandenburger and Stuart (1996) who, in particular, discussed the utility o the value-added concept in analyzing business strategy; also see Brandenburger and Stuart (2006), and MacDonald and Ryall (2004b). Lippman and Rumelt (2003) explore the bene ts o coalitional game theory or strategy research and compare various well-known equilibrium concepts or coalitional games. Gans, MacDonald and Ryall (2005) show how the coalitional ramework can be used in practice and elaborate on the interpretation o the mathematical primitives o the coalitional model. Adner and Zemsky (2006) use value-added concepts to analyze the sustainability o competitive advantage. De Fontenay and Gans (2004) use coalitional game theory to analyze the strategic implications o outsourcing. We begin with examples illustrating the basics o the methodology and some o our results, then develop the ormal notation, review the basic characterization result, and discuss the new results. 2 Examples 2.1 Pre-entry game The pre-entry game includes a rm, ; and two buyers. The rm has one unit o production capacity, and can costlessly produce either one o two goods, which we will think o as components o a system o some sort. For example, the goods might be a video device and a plasma TV. Buyer 1 has some use or one o the goods, valuing it at $10, but also values the whole system, at $30. Buyer 2 has no use or either good on its own, but also values the system at $30. Let i denote the appropriation o buyer i = 1; 2 and that o the rm. In all that ollows, we assume ; 1 ; 2 0: Then, the conditions describing competitive appropriations, ; 1 and 2 are ; + 2 0; ; 6

7 and = 10: (Since there is just one unit o capacity, the $30 value o the system cannot be achieved.) Observe that buyer 2 s added value (i.e., the aggregate value the whole group can generate, less the value and buyer 1 can generate on their own) is zero. Thus, since an agent s appropriation is bounded above by his/her added value, 2 = 0: Excluding redundant constraints, we have ; and + 1 = 10: It ollows immediately that 0 10 and 1 = 10 : In particular, does not have competitive advantage under our de nition since = 0 is consistent with these conditions. The remaining examples illustrate how entry might eliminate or create competitive advantage. 2.2 Entry eliminates competitive advantage Now assume an entrant, e; joins the game, and that e has precisely the same capabilities as in the sense that buyers do not care whether they purchase rom or e: However, in this example, we assume that compatibility issues mean that a system must be purchased rom one rm, i.e., a buyer could purchase one unit rom each rm, but buyer 1 would generate $10 buy doing so, and buyer 2 would generate $0. Excluding redundant constraints, the conditions describing competitive appropriations, ; e ; 1 and 2 are ; e ; + e ; ; e ; and + e = 10: 7

8 Suppose appropriates, i.e., > 0: Then, there is strictly less than $10 let to be distributed among e and the buyers. But e s entering and having the same capabilities as means that generating $10 is always an option or e and the buyers. This implies that they can improve on any distribution o value that leaves them appropriating less than $10. Thus e s entry guarantees cannot appropriate. In this example, entry brought more capacity, but, as a result o the incompatibility, not in a way that allowed any more value to be achieved. Moreover, entry did not create any valuable alternative or the and e pair alone, since buyer 1 is needed to create value. Further, as a result o the incompatibility, entry did not open up any new alternatives or groups o agents including ; e.g. by including e; the group o and either buyer can create the same value they could without e: The only new alternatives created by e s entry involve groups not including ; i.e., e with buyer 1, or buyer 1 and buyer 2. Under these circumstances entry can never create competitive advantage or ; and, indeed, orces s appropriation to zero (see Proposition 6 or the general statement). This example, while very special, typi es the kind o outcome that motivates much concern about entry. That is, entry merely creates new opportunities or agents other than ; thereby creating competition that restricts or eliminates the possibility o appropriating. The next examples show that the situation need not be much di erent or entry to have a very di erent impact. 2.3 Entry creates competitive advantage In this example we continue to assume e s product is not compatible with s, but in a less extreme manner. That is, buyer 2 continues to value the incompatible products at $0, but buyer 1 can achieve $11 in value rom both goods, and $10 rom just one. We also suppose that a system, but neither good individually, has some alternative use outside the game, valued at $2. Excluding redundant constraints, the conditions describing competitive appropriations become 4 4 The value 0 on the right hand side o + e + 2 0, along with e + 2; implies that this game is not superadditive. The value can be changed to 2 without altering any 8

9 e + 2; ; e ; + e ; ; e ; and + e = 11: Suppose = 0. Then, i the outside alternative available to and e is to be unattractive, e must appropriate at least $2; leaving at most $9 or the buyers. But this makes buyer 1 s option o buying one unit rom quite attractive. Thus, must appropriate. In act, in this example the unique competitive appropriations are = e = 1, 1 = 9 and 2 = 0. That is, and e must appropriate at least $2 between them, leaving at most $9 or buyer 1. But each o and buyer 1, and and buyer 2, can appropriate $10 between them. and e receiving exactly $1 is the only way to divide $11 in the required ashion. In this example, entry allowed more value to be achieved, but also opened up a new opportunity or e and. On net, the tension between extra value to be distributed and better alternatives to the equilibrium activities result in having competitive advantage where none existed beore. (This case is generalized in Proposition 7.) 2.4 Entry creates even greater competitive advantage Finally, we assume that entry does not yield a new outside use or the system, but that the goods are ully compatible. The nonredundant conditions describing competitive appropriations are ; e ; + e ; + e ; ; e ; o what ollows. The zero value makes the example exactly consistent with the hypotheses o Proposition 7. Likewise, + e is required or the interpretation o the example, but does create an inconsistency with the hypotheses o Proposition 2; however, this inequality plays no role in determining the minimum appropriation or. 9

10 and + e = 30: Post-entry, since either buyer values the whole system, both have zero added value, and so 1 = 2 = 0: Conditions describing competitive appropriations simpliy to 10; e 10; + e 30; and + e = 30; i.e., and e = 30 : Pre-entry, s appropriation lay between 0 and $10; post-entry, s appropriation lies between $10 and $20, i.e., entry not only created competitive advantage but actually shited the incumbent s entire range o appropriation or the better. The intuition is as ollows. Pre-entry, there is not enough capacity to produce anything buyer 2 values, so and buyer 1 are e ectively in a pure bargaining situation. Thus, whatever appropriates is not a consequence o competition, and does not have competitive advantage. Post entry, there is su cient capacity to produce the system, which both buyers value at $30. Speci cally, and e each produce to capacity, and one buyer purchases a system. Buyers have become intense competitors each having zero added value and so the $30 must be shared between and e: The sole constraint is that this sharing is such that neither nor e could improve by selling one good to buyer 1 instead o being part o ormation o a system. In this example (consistent with the generalization in Proposition 8), an entrant both allows more value to be created (i.e., $30 versus $10) and opens up new alternatives ( and e together have capacity to create $30 total with either buyer). The ormer tends to lower s minimum equilibrium payo, whereas the latter tends to increase it. In this example, the latter dominates, and entry creates competitive advantage. 10

11 3 Preliminaries 3.1 Notation and assumptions Our goal is to study the value appropriation possibilities or an agent, or example, an incumbent rm, beore and ater the entry o another agent. The entering agent could be an imitating rm, but there are lots o other possibilities a new supplier, a new customer, a rm o ering a complementary product,... The coalitional game ramework we employ is general enough to accommodate any kind o entry. 5 The simplest and most transparent way to carry out the analysis involves speciying the post-entry game in detail, and then comparing pre-and post-entry appropriation possibilities or the agent o interest by treating the pre-entry case as the special one in which (in a way that will be made precise shortly) the entering agent has been suppressed. To that end, we assume the game has n + 1 agents, indexed by i; i = 1; :::; n + 1 < 1. Given the players, the balance o the speci cation o any coalitional game involves a description o the value that is expected ultimately to be created by the agents the aggregate value that will be appropriated by the agents in the game as well as the value o the alternatives that are available to subgroups o the agents. The idea is that the value any group o agents will ultimately appropriate must exceed or equal what that same group could obtain by acting on alternatives available to it. Otherwise, why would that group not act on its alternative instead? We begin by describing all the possible groups o agents in a way that acilitates analysis o the pre- and post-entry games. Then, we speciy the value that will ultimately be distributed and the value subgroups o agents can obtain rom available alternatives. We employ (n + 1)-length vectors o zeros and ones to describe the groups, where a vector with a 1 in the i th position means the group includes agent i; a generic vector will be labelled g; and entities associated with g will have a 5 The basics o this ramework are explained at length in MacDonald and Ryall (2004); also see Brandenburger and Stuart (2003). 11

12 g-subscript. It will be clear rom the context whether g is a row or a column. The agent whose appropriation we will ocus on will be the rst in any such vector, and the entrant the last. For concreteness, we will call the rst agent the incumbent rm, ; and the last agent the entrant, e: The analysis o the pre- and post-entry games is acilitated by organizing all the possible groups o agents in a particular way. The group o all agents is I (1; 1; :::; 1) : The group including only is I (1; 0; :::; 0) ; whereas the group o all agents other than is I (0; 1; :::; 1) : Analogously, the group including only e is I e (0; :::; 0; 1) ; and the group o all agents other than e is I e (1; :::; 1; 0) : The group including only and e is I e (1; 0; :::; 0; 1) ; and the group including all agents other than and e is I e (0; 1; :::; 1; 0) : This leaves 2 n+1 8 groups that include at least one, but not every, agent other than and e; and possibly one or both o and e: These groups can be divided into our subsets, each consisting o 2 n 1 2 groups. The rst subset is the collection o groups that include but not e: This collection can be described by the 2 n 1 2 (n + 1) matrix [1G0] ; (1) 12

13 where 1 (0) is a column vector o ones (zeros) o length 2 n 1 2 and G is the 2 n 1 2 (n 1) matrix in which no two rows are the same and no row is either all zeros or all ones. Similarly, the collections o groups that include neither nor e is described by [0G0] ; (2) those including e but not are [0G1] ; (3) and those including both e and are [1G1] : (4) Any o the groups can produce value on its own in the sense that agents in the group can engage in whatever transactions are technically and institutionally easible. For any group, g; v g denotes the value that can be generated by g: Hence, the aggregate value anticipated in the post-entry industry is v I ; the value available to agent i acting alone is v Ii ; and so on. We assume, without loss o generality, that v Ii = 0 (a normalization). There are 2 n+1 1 distinct and nonempty groups o players that can be ormed rom n + 1 players. Let v be the 2 n+1 1 -vector o nonnegative numbers in which each component corresponds to a nonempty group; i.e., v is a vector including the v g values, or all g: Consistent with the group-identi cation scheme introduced above, v I is the value that can be produced by the rm on its own, v I the value that can be produced by all the agents without the rm, and so on. Similarly v 10 is the 2 n 1 2 -length vector that includes the components o v corresponding to the rows o (1); v 00 is the vector that includes the components o v corresponding to the rows o (2); etc. Note that v includes all inormation on the value creation opportunities available to the agents in both the pre- and post-entry games. That is, v I is the aggregate value that will be produced in the industry post-entry. The other components o v (including v I e ) are the values that any subgroup g could obtain 13

14 on its own in the post-entry game. Likewise v I e is the aggregate value that will be produced in the industry pre-entry, i.e., e is not active in the pre-entry game. Other components o v, corresponding to groups g that do not include e; are the values that these groups could obtain on their own in the pre-entry game. Finally, to avoid trivial cases, we assume that any group g is no less productive when either or e is included: or all groups g not including v g+i v g ; (5) and or all groups g not including e v g+ie v g : (6) 3.2 Competitive distributions and appropriation Whatever economic activity ultimately transpires either pre- or post-entry the resulting value will be appropriated by the participating agents. Let be an (n + 1)-vector describing each agent s appropriation; is called a distribution o value. We will reer to s (e s) appropriation as ( e ). A distribution o value, ; is easible and stable in the pre-entry game i: I v I e ; (7) and, I 0; (8) I e v I e ; (9) I e v I e ; (10) [1G0] = v 10 ; (11) [0G0] = v 00 : (12) Condition (7) is the easibility condition, requires that only the value agents can produce without the entrant, v I e ; be distributed among the other agents. The 14

15 other conditions, (8) (12), are the stability conditions. They are necessary i, given ; agents are assumed to participate voluntarily in producing v I e : The logic behind this is that, i any o (8) (12) ail, there is some group, g; not including e; or which g < v g. That is, the agents in g could all be made strictly better o by not participating in the contemplated transactions (i.e., whatever produces value v I e ) and, instead, producing v g via some other activity. (8) (12) is a complete description o the competitive opportunities and alternatives players have that do not involve e: For what ollows, it is useul to recall a some basics about competitive distributions in coalitional games. One is that or any agent, say ; the levels o appropriation or that agent that are consistent with competition (i.e., is a easible and stable distribution) orm a closed interval, i.e., a lowest possible value, a highest possible value, and everything between. We denote this interval by [ min ; max ]. Generally, min determine the rm s appropriation uniquely. To determine the rm s appropriation when min < max ; i.e., competition does not normally < max ; additional assumptions are required regarding the resolution o super-competitive actors. 6 Second, i there is more value to distribute e.g., v I e is larger the interval o appropriation or consistent with competition cannot shrink, and generally grows. Third, i the alternatives available to agents improve e.g., any o the components o v I e ; v 10 or v 00 increase the interval o appropriation or consistent with competition cannot grow, and generally shrinks. Finally, and more speci c to the pre- and post-entry setup studied here, (7) and (9) imply that exactly v I e is distributed among the agents in the pre-entry industry, and that e = 0. (I e > 0; (7) requires that strictly less than v I e be distributed among the agents in the pre-entry game, violating (9).) 7 6 See Brandenburger and Stuart (2004) or a very intuitive and applicable approach. Since we are concerned only with the e ects o competition on the value appropriated by industry participants, we leave open the question o how extra-competitive issues are resolved. 7 The last conclusion is straightorward, but important in the sense that it would be hard to interpret (7)-(12) as describing a competitive situation where the entrant plays no role i e > 0 were possible. 15

16 A distribution o value, ; is easible and stable in the post-entry game i (7) is replaced by I v I ; (13) and, in addition to (8) (12), satis es I e 0; (14) I v I ; (15) I v I ; (16) I e v Ie ; (17) [1G1] = v 11 ; (18) [0G1] = v 01 : (19) Condition (13) replacing (7) accounts or the act that post-entry, v I is available or distribution instead o v I e : Including (14) (19) takes account o the act that the entrant opens up new alternatives or players, while removing none, and that i a distribution, ; is to survive competition, these new alternatives must not o er any group the prospect o improvement over what o ers. 8 h i Let ; ^ max be the range o appropriation or that is consistent with ^ min competition post entry. That (13) replaces (7), and (14)-(19) are in addition to (8) (12), oreshadows the two general e ects that an entrant has on an incumbent s appropriation possibilities. First, since (6) implies v I v I e ; there is no less, and generally more, value to distribute post entry. This, by itsel, tends to expand the range o appropriation or that is consistent with competition. On the other hand, post-entry, agents have many alternatives i.e., those involving e that were unavailable pre-entry; this, by itsel, has the same sort o impact as improving agents alternatives pre-entry, i.e., it narrows the range o appropriation or that is consistent with competition. The net e ect o e s presence on re ects 8 Notice that (13) and (15) imply I = v I : We assume that there is at least one competitive distribution in each o the pre- and post-entry games. 16

17 the relative strength o these two orces; our results explain how this relative strength is determined. 4 Competitive advantage I every easible and stable distribution has appropriating more than its nextbest alternative (here normalized to 0), then is guaranteed an economic pro t, i.e., min > 0. In this case the orces o competition alone guarantee economic pro t no matter how the extra-competitive orces mentioned above operate. Whenever min > 0, we will say that the incumbent has a competitive advantage, where we emphasize that s value appropriation is guaranteed by competition. When does not have a competitive advantage, de ned in this way, might still appropriate, provided max > 0; however, any value appropriates in this case will be a consequence o some supra-competitive activity like bargaining, airness or luck, and not the consequence o competition. It helps to have some notation to keep track o whether and when has a competitive advantage. So CA pre means min > 0, and CA post means ^ min > 0: In earlier work (MacDonald and Ryall (2004)), we provided a complete characterization o when a player in an arbitrary coalitional game has a competitive advantage as just de ned. Since this basic result applies to and to both the pre- and post-entry games, it will be helpul brie y to review that result, since it necessarily plays a key role in what ollows. 4.1 Characterization (MacDonald & Ryall, (2004)) Agent ailing to have a competitive advantage in the pre-entry game is equivalent to the existence o a distribution, ; satisying (7)-(12), and or which = 0: This observation allows us to characterize CA pre ; a characterization o CA post ollows analogously. To see how the characterization works, assume = 0: Then (8) is always satis ed; using (5), i (9) is satis ed then (10) is too; and, again employing 17

18 (5), i (11) is satis ed then (12) is too. Combining (7) and (9), the conditions whose satisaction is equivalent to not having a competitive advantage in the pre-entry game are simply I e = v I e and [0G0] = v 10 ; (20) where the latter is (11), taking account o the act that when = 0; [1G0] = [0G0] : Inequalities (20) require that ; with = 0; distributes value so that no group o agents (where e is not a member o any such group, since we are considering the pre-entry game) could appropriate more value by acting on some alternative including : These are the most attractive alternatives since would be no worse o by being included, and every such alternative is at least as valuable when is included (i.e., (5)). Now notice that i there is su cient value to distribute, i.e., v I e is large enough, then (20) can always be satis ed, i.e., CA pre does not hold. Thus, CA pre holds i and only i v I e is not too large. More precisely, let mv pre min 2R n+1 + I j [0G0] = v 10 g : (21) mv pre is called s minimum value in the pre-entry game, and is the least value that can be distributed to players other than and e, while simultaneously making none o the alternatives described by (20) attractive. 9 I mv pre is larger than the value available or distribution, v I e ; there is no easible way to distribute value, with receiving nothing, without making some alternative attractive to some group including ; thus, must appropriate. Conversely, i appropriates in every easible and stable distribution, then the available resources must be too meagre to distribute without making some alternative attractive to some group including i = 0: 9 As stated, the minimation problem does not require = e = 0; however, any minimizing will have this eature. 18

19 Theorem 1 (MacDonald and Ryall) CA pre i and only i mv pre > v I e : Analogous reasoning can be applied to ailing to have a competitive advantage in the post-entry game. I this is the case, there is a distribution, ; satisying (8)-(19) and that has = 0: To develop the equivalent to Theorem 1, assume, again, that = 0: Then, as above, (8) is satis ed. Also, (10) is satis ed i (9) is, which, since I e = I e when = 0; we will write I e v I e : (22) Similarly, (11) and (12) can be combined, exactly as above, to yield (20). Next, (16) is satis ed i (15) is, and (13) and (15) together imply that, post entry, exactly v I will be distributed: I = v I : (23) Also, (14) is satis ed i (17) is, which, using I e = I e ; we write as Finally, using (5), (19) is met i (18) is: I e v Ie : (24) [0G1] = v 11 ; (25) where, as above, we note the act that when = 0; [1G1] = [0G1] : Thus, the question o whether has a competitive advantage in the post-entry game can be answered by determining whether the value that might be distributed, as described by (23) are su cient to allow (20), (22), (24) and (25) to be satis ed. De ne mv post min I j I e v I e ; I e v ; [0G1] = v Ie 11 and [0G0] = v 10 : 2R n+1 + (26) Theorem 2 (MacDonald and Ryall) CA post i and only i mv post > v I : Note that the minimization problems (21) and (26) have the same objective, and that the constraints in the ormer are a subset o those in the latter; thus mv pre mv post : Moreover, in (26) the aggregate value distributed to agents other than or e must be at least v I e ; thus mv post v I e : 19

20 Lemma 1 mv post maxmv pre ; v I e g: Finally, observe that (6) implies v I v I e : De ne e s added value by av e v I v I e ; (6) implies av e 0: 5 The impact o entry on competitive advantage 5.1 Basic result Given Theorems 1 and 2, Lemma 1, and the act that v I v I e ; we can be speci c about the impact o entry on s competitive advantage. There are exactly our entities that, together, determine this e ect: mv pre ; mv post ; v I and v I : e Proposition 1 Given the pre- and post-entry games, entry 1. destroys competitive advantage CA pre and not CA post i and only i both mv pre > v I e and mv post v I ; 2. creates competitive advantage not CA pre and CA post i and only i mv pre v I e and mv post > v I ; and 3. sustains competitive advantage CA pre and CA post i and only i mv pre > v I e and mv post > v I : Remark 1 Given the pre- and post-entry games, entry does not sustain, create, or destroy competitive advantage neither CA pre nor CA post i and only i mv pre v I e and mv post v I : Given Proposition 1, there are two sources o insights about how entry impacts s competitive advantage. One is urther exploration o Proposition 1 20

21 itsel. 10 The other is exploration o the sources o the di erent patterns o values and minimum values that lead to the di erent cases in Proposition 1. We examine these in turn. 5.2 Examination o proposition 1, part 1 Since result (1) implies mv post mv pre ; the inequalities in part 1 o Proposition 1 can be combined to yield v I mv post mv pre > v I e : Subtracting v I e throughout, then applying the de nition o av e ; yields the ollowing proposition. Proposition 2 Given the pre- and post-entry games, entry destroys competitive advantage i and only i av e mv post v I e mv pre v I e > 0: Two observations ollow immediately. First, an entrant whose added value is su ciently large always destroys s competitive advantage. The intuition is straightorward. Entry provides agents both new alternatives which, as discussed earlier, tends to increase min along with more value, which has the opposite e ect. I av e is large enough, the latter e ect always outweighs the ormer. Second, i the entrant is to destroy competitive advantage, a strictly positive av e is necessary (the theoretically smallest possible value or av e is zero). The argument is easy. I has a competitive advantage in the pre-entry game, the reason is that, assuming does not appropriate, the alternatives available to agents are too valuable to be dominated with the available resources. Entry produces even more alternatives. So i the entrant brings no new value to the game, i.e., av e = 0, the same orces that gave competitive advantage pre-entry are augmented by entry. Since the resources available to oppose these orces are no greater, must continue to appropriate post-entry. 10 Corollaries (2)-(5) below, being corollaries, ollow immediately rom Proposition 1. However, in each case a small calculation is required. These calculations are included as ootnotes. 21

22 The necessity o av e > 0 or entry to destroy s competitive advantage provides an interesting perspective on a amiliar situation in which entry is thought to eliminate competitive advantage. Consider a monopolist, ; with a constant returns production technology, and a collection o customers, at least some o whom value the monopolist s product at more than its (constant) marginal cost. Now assume another rm enters, o ering the same product, and having the identical constant returns technology. Given identical costs and constant returns, the entrant has av e = 0; and so, according to Proposition 2, cannot destroy competitive advantage. But given the identical products and costs, it is immediate that ^ min = ^ max = 0; i.e., has no competitive advantage post-entry. These conclusions are mutually consistent only i had no pre-entry competitive advantage. That is, the orces o competition in the pre-entry game did not guarantee the monopolist could appropriate. This is exactly correct. Given constant marginal cost, the monopolist is e ectively in a pure bargaining game with every consumer, where the bargaining is over the surplus (value less production cost) rom that one transaction. Thus min = 0 and max = S; where S is the aggregate surplus rom consumption o the good by all consumers who value it at marginal cost or more. In this situation any pro t the monopolist extracts rom consumers pre-entry is purely the result o bargaining/negotiation, and not a consequence o the competitive alternatives available to it or to consumers. 11 The orces o competition are very weak preentry, and, in particular, has no competitive advantage. Entry does nothing to make competition to transact with more attractive, and creates an alternative or consumers that makes bargaining with unnecessary, and, in act, orces = e = 0: Entry did not destroy the ability o alternatives to guarantee appropriation or. Instead, it eliminated the possibility o appropriating via 11 Speci cally, the textbook monopoly model assumes the rm has all the bargaining power. However, given constant returns, the monopolist s threatening, or example, to exclude one customer and sell to another is not credible, and there is no obvious justi cation or the bargaining power assumption. With increasing marginal cost or capacity constraints, this assumption has greater justi cation. At the same time, with increasing marginal cost, entry generally does not remove competitive advantage. 22

23 bargaining. 5.3 Examination o proposition 1, part 2 Since (6) implies v I v I e ;the inequalities in part 2 o 1 can be combined to yield mv post > v I v I e mv pre : Subtract v I e throughout and, as beore, apply the de nition o av e. Proposition 3 Given the pre- and post-entry games, entry creates competitive advantage i and only i mv post v I e > av e 0 mv pre v I e : Using result (1) and the act that has no pre-entry competitive advantage, the theoretically smallest value mv post can take on is v I e ; so mv post v I e is mv post measured relative to its smallest possible value. Two observations ollow rom Proposition 3. First, i entry generates new alternatives or groups including that are su ciently valuable, in the sense that mv post v I e is large, then always has competitive advantage post-entry. In this case, although the additional resources entry brings make it easier or given alternatives involving to to be dominated, entry also o ers new alternatives. And i these alternatives are valuable enough, must appropriate post-entry even i ailing to do so was possible pre-entry. Second, or entry to create competitive advantage, it is necessary that mv post be strictly greater than its smallest possible value, v I e : I mv post = v I e ; then the resources available to render unattractive the new alternatives entry brings, i.e., v I ; are ample and need not appropriate. Return to the example o monopoly with entry. In that example, mv post = S(= v I e = v I ): So, consistent with what we ound beore, entry has no prospect o creating competitive advantage or : Altogether, in the monopoly with entry example, entry neither creates nor destroys competitive advantage. 23

24 5.4 Examination o proposition 1, part 3 Since (6) implies v I v I e ; the second inequality in part 3 o Proposition 1 gives mv post > v I v I e : Subtracting v I e throughout, then applying the de nition o av e ; gives mv post v I e > av e 0: The rst inequality in part 3 o Proposition 1 is equivalent to v I e mv pre < 0: This, with the previous inequalities, yields the ollowing result. Proposition 4 Given the pre- and post-entry games, entry sustains competitive advantage i and only i mv post v I e > av e 0 > v I e mv pre : The intuition or Proposition 4 is as ollows. The orces o competition preentry were strong enough to allow competitive advantage. Post-entry there is more value to distribute, but the existing and new alternatives involving continue to be too attractive or s not appropriating to be stable. Finally, we present a proposition demonstrating that the two opposing orces that we have emphasized thus ar are indeed all the orces determining entry s impact on competitive advantage. I entry a ects competitive advantage, it either creates it or destroys it. In the ormer, both mv pre v I e and mv post > v I ; or In the latter both mv post mv pre > av e : mv pre > v I e and mv post v I ; 24

25 or mv post mv pre < av e : We combine these to conclude the ollowing. Proposition 5 Given the pre- and post-entry games, i entry a ects competitive advantage, it creates it i and only i mv post mv pre > av e ; and destroys it i and only i mv post mv pre < av e : The let hand side o each inequality measures the impact o increased competition to create value with that entry brings, and the right hand side describes the additional resources that might be used to resolve this competition. 5.5 Impact o the new alternatives entry brings Earlier we showed that minimum value i.e., the least value that can be distributed to agents other than (i.e., receives zero) without making some alternative including preerable or some group was one o the two actors determining whether had comparative advantage; the minimization problems (21) and (26) yield minimum value in the pre- and post entry games, respectively. Compared to the pre-entry game, entry introduces exactly three new kinds o alternatives, described by (22), (24) and (25), that in uence minimum value. In this subsection we explore, one at a time, how these new alternative work, or ail, to in uence s competitive advantage. As discussed earlier, entry impacts s competitive advantage through bringing new resources, and also changing the competition or s participation. Our ocus in this subsection is solely on the latter, i.e., how and whether the new alternatives work to increase competition or ; and thus s minimum value and competitive advantage. 25

26 The rst new alternative, (22), is the one that involves all agents other than e; including ; simply acting on their own and sharing v I e : Whereas the agents other than e ultimately (i.e., a requirement o equilibrium) had to share v I with pre-entry, post-entry, doing this is simply one o the available alternatives. Does this new choice, by itsel, have any particular e ect on s competitive advantage? Intuitively, the answer must be no. That is, when the entrant does not make any group including more valuable, it does nothing to make the alternatives involving any harder to dominate, which leaves s minimum appropriation, at best, unchanged. So i lacks competitive advantage preentry, e s participation cannot create competitive advantage: On the other hand, i has competitive advantage pre-entry, the act that the entrant generally has a positive added value means there are more resources available, which, or the reasons set out earlier, tends to erode s competitive advantage. these additional resources are great enough, s competitive advantage might be destroyed. Overall, sharing v I e with becoming an alternative rather than a necessity can never create competitive advantage. Indeed, entry allowing s competitive advantage to persist is the best can hope or. More ormally, assume both v Ie = 0 and v 11 = v 10 : That is, the alternatives available to to any group including (other than the group o all agents except e) are not improved by including e: Under these assumptions, (26) becomes 12 mv post 1 min I j I e v I e and [0G0] = v 10 ; (27) 2R n+1 + i.e., comparing (27) to (21), I e v I e is the sole additional constraint that has any bearing on the magnitude o mv post 1 ; and thus on the mv post 1 versus v I comparison that determines whether has competitive advantage post-entry. Proposition 6 Given the pre- and post-entry games, i v Ie = 0 and v 11 = v 10 ; entry 12 To see this, observe that when v 11 = v 10 ; any satisying [0G0] = v 10 also satis es [0G1] = v 11 ; but not the converse. Thus the latter set o inequalities can be eliminated rom (26). e I 26

27 1. Does not create competitive advantage; 2. Destroys competitive advantage i and only i v I e < mv pre v I ;and 3. Sustains competitive advantage i and only i v I < mv pre : The argument is as ollows. For part 1, suppose does not have competitive advantage pre-entry, i.e., mv pre v I that satis es [0G0] = v 10 and I e v I e. Then there is at least one distribution e : Thus the minimum value in (27) can be achieved by some distribution satisying [0G0] = v 10 and also I e = v I advantage post-entry. e ; i.e., mv post 1 = v I e : Since v I e v I ; has no competitive For part 2, suppose has competitive advantage preentry, i.e., mv pre > v I e : It ollows that any minimizing distribution in (27) also has I e > v I e ; in which case (21) and (27) are the same problem, i.e., mv post 1 = mv pre : Thus, whether also has competitive advantage postentry hinges on a comparison o v I and mv pre : This also settles whether entry sustains competitive advantage, i.e., part 3. An example to which Proposition 6 applies is as ollows. Imagine that the pre-entry game describes a collection o rms, including ; that have ormed a joint venture to develop some technology, and whose capabilities are such that no subgroup o the agents can develop the technology completely. Assume that the entrant joining the game permits greater value to be achieved rom the ully developed technology, but no more to be derived a partially-developed version; e.g., the entrant introduces a new or enhanced use or the technology. Then, the arrival o the new agent cannot create competitive advantage or ; and might even destroy it, even i has some capability that is central to developing the technology. A similar example ollows i the pre-entry agents are engineering teams assigned to develop the next generation o a microprocessor, and the entrant is a sotware developer whose work can make the ully-unctioning microprocessor more productive. Next, what happens when e s entry provides a valuable alternative or, but does not improve alternatives or any groups including and other existing 27

28 agents (except possibly the group o and all existing agents, i.e., av e > 0). That is, is missing something that e can provide, but other agents might also ll this gap, so that adding e is only impactul absent other agents. How will this a ect s competitive advantage? Intuitively, e s participation provides an alternative that might be attractive to the pair and e: This will improve the total appropriation possibilities or that pair. But it may not create competitive advantage or i it was not already present, since e doing most or all o the o the appropriating is a possibility. It ollows that i e s entry creates a valuable alternative or the pair and e; but it is not possible or e to appropriate much, then entry will either create, or at least sustain competitive advantage or : What would stop e rom appropriating much? Small av e : Proposition 7 ormalizes and sharpens this intuition. To see how, consider the group including only 13 : Pre-entry, this group s alternative is just v I = 0; whereas post-entry and e can share v Ie : Once again assuming v 11 = v 10, but allowing v Ie > 0; mv post 2 min I j I e v I 2R n+1 + e ; I e v and [0G0] = v Ie 10 : (28) Proposition 7 Given the pre- and post-entry games, i v 11 = v 10 ; entry 1. Creates competitive advantage i and only i mv pre v I e 0 av e < v Ie ; 2. Destroys competitive advantage i and only i 0 < mv pre v I e v Ie + mv pre v I e av e ; 13 To determine the impact on s competitive advantage o the option o all players other than e; including ; simply acting on their own and sharing v I e ; we set v Ie = 0 and v 11 = v 10 ; e ectively prohibiting v Ie and v 11 rom having any impact. To examine their impact alternative by alternative, it is tempting to do so while prohibiting the constraint I e v I e rom having any impact, say by setting v I e = 0: This would be a mistake. Assuming v Ie = 0 and v 11 = v 10 simply structures how the pre- and post-entry games di er. Assuming v I e = 0 undamentally changes the pre-entry game. Thus, the next two Propositions make no new assumption about v I e : 28